Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. P= (b) Use the matrices P and A to find [v]g and [7(V)]B, where [v]= [-14]. [v]8 = [T(V)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = QED 1 A¹ = 1
Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let A = 02 be the matrix for T: R2 R2 relative to B. (a) Find the transition matrix P from B' to B. P= (b) Use the matrices P and A to find [v]g and [7(V)]B, where [v]= [-14]. [v]8 = [T(V)]8 = (c) Find P¹ and A' (the matrix for 7 relative to B'). p-1 = QED 1 A¹ = 1
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter6: Linear Systems
Section6.3: Matrix Algebra
Problem 85E: Determine if the statement is true or false. If the statement is false, then correct it and make it...
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![Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let
A =
02
be the matrix for T: R² R2 relative to B.
(a) Find the transition matrix P from B' to B.
P=
(b) Use the matrices P and A to find [v]g and [7(V)]B, where
[v] = [-14].
[v]8 =
[T(v)]8 =
(c) Find P¹ and A' (the matrix for 7 relative to B').
p-1 =
A¹ =
1
1
↓↑
(d) Find [T(v)] two ways.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ff821f9aa-4788-41c9-90a4-53f493bbfa90%2F7caddd56-aae0-485b-85e6-bd5aae54ed25%2Fn4vsndo_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Let B = {(1, 3), (-2,-2)) and B' = {(-12, 0), (-4, 4)) be bases for R2, and let
A =
02
be the matrix for T: R² R2 relative to B.
(a) Find the transition matrix P from B' to B.
P=
(b) Use the matrices P and A to find [v]g and [7(V)]B, where
[v] = [-14].
[v]8 =
[T(v)]8 =
(c) Find P¹ and A' (the matrix for 7 relative to B').
p-1 =
A¹ =
1
1
↓↑
(d) Find [T(v)] two ways.
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